Determination of the frequency of laser radiation

ABSTRACT

A method enabling the frequency of the radiation emitted by a multi-frequency CO2 laser to be determined with precision by adjusting the optical length of the resonant cavity, so as to be a multiple of the wavelengths of the two beams emitted, and so as to obtain a central dip in the power curve for one of the beams.

United States Patent 91 Vautier et al.

[451 Jan. 16, 1973 DETERMINATION OF THE FREQUENCY OF LASER RADIATION[75] Inventors: Philippe Jean Vautier; Jean Yves Coester, both of Paris,France [73] Assignee: Societe Anonyme De Telecommunications, Paris,France [22] Filed: Dec. 1, 1970 [21] Appl. No..* 93,930

[30] Foreign Application Priority Data Dec 5, 19 69 France ..6942107Feb. 5, 1970 France ..7004088 [52] US. Cl ..33l/44.5, 350/l60 [5 [1 Int.Cl.... ..II01S 3/10 [58] Field of Search ..33 l/94.5; 350/160 [5 6]References Cited UNITED STATES PATENTS 3,534,292 10/1970 Cutler..33l/94.5

Primary Examiner-William L. Sikes Attorney wenderoth, Lind & Ponack [57]ABSTRACT A method enabling the frequency of the radiation emitted by amulti-frequency CO laser to be determined with precision by adjustingthe optical length of the resonant cavity, so as to be a multiple of thewavelengths of the two beams emitted, and so as to obtain a central dipin the power curve for one of the beams.

3 Claims, 6 Drawing Figures PATENTEDJAR 15 ms 'F/aa PHILIPPE JEANVAUTIER and JEAN YVES COESTER, Inventors Attorneys PATENTEDJAH 16 I9753.711.786

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PHILIPPE JEAN VAUTIER and JEAN YVES COESTER, 'Inventcis AttorneysPATENTEDJAH 16 I975 SHEET 3 UF 4 a Q 2 &

PHILIPPE JEAN VAUTIER and JEAN YVES COES'I'ER, Inventors AttorneysPATENIEDJM 16 I975 3.711.786

' SHEET l UF 4 FIG 6 PHILIPPE JEAN vmd'maa an; JEAN YVES COESTER, Inven'ors Ml/MMHIMZ 1M Attorneys DETERMINATION OF THE FREQUENCY OF LASERRADIATION FIELD OF THE INVENTION The present invention relates to amethod and apparatus for determining the optimum length of the resonantcavity of a carbon dioxide gas laser apparatus as a function of thewave-length selected for use from the variety of wave-lengths of whichthe emission from said laser apparatus may be composed, said varietybeing known as the multifrequency.

BACKGROUND OF THE INVENTION It is known that the output power curve of asinglebeam and single-mode laser bends downwardly, as a function offrequency, when passing through the central transition frequency. Thisdownward bend, known as the Lamb dip, is the subject of an article byW.E. Lamb that appeared in 1964 in Jr. Phys. Rev., No. 134, page A1,429. Observation. of this phenomenon, which is simple in a HeNe laser,requires several additional precautions in the case of the carbondioxide gas laser. In effect, since the carbon dioxide gas laser oftenemits a multi-frequency radiation, the Lamb dip phenomenon is masked bya more clearly observable phenomenon, the observations of which formedthe subject of a communication to the French Academie des Sciencesduring the session on 24th Nov. 1969, under the title: Interpretation ofdips observed in the profile of CO laser beams," by Philippe Vautier,Jean Coester and Pierre Barchewitz.

In fact, the output power of the laser, recorded at a fixed wave-length,as a function of the length of the cavity, constitutes a succession ofpeaks at intervals of M2. When the laser simultaneously emits severalwavelengths, the power in each of the beams undergoes periodicvariations in amplitude, and the lower the pressure within the laser andthe stronger the internal field at the cavity, the more pronounced arethese variations. If the wave-lengths are known, it is possibletheoretically to establish the coincidence pitch of adjacent beams:

Beam Number of peaks Coincidence pitch Pl4/Pl6 P16: 546 peaks 2.87 mmP14: 547 peaks Pl6lPl8 PIS: 537 peaks I 2.83 mm H6: 538 peaks Pl 8/P20P: 529 peaks 2.79 mm Pl 8: 530 peaks P20/P22 P22: 521 peaks 2.76 mm P20:522 peaks P22IP24 P24: 5l2 peaks 2.72 mm P22: 513 peaks k, and k beingwhole numbers and n the index of the resonant cavity. This relationshipcan, however, be extended to cover the case of the emission of severalbeams of different wave-length:

255 761 1 2M ki n SUMMARY OFTHE INVENTION The method of the presentinvention is based upon the use of this latter physical phenomenon,wherein a central dip appears in the output power/frequency curve of oneof the beams of a carbon dioxide gas laser operating simultaneously withseveral beams each in a single mode.

The method of the present invention employs this relationship in thecase of emission on two, three or more wave-lengths, associated withrespective laser beams, and it is characterized in that the opticallength of the resonant cavity is, on the one hand, a multiple of thewave-lengths of the laser beams generated in said cavity and, on theother hand, is adjusted in such manner as to obtain a central dip at apoint between two peaks of equal amplitude in the power curve of one ofthe beams.

In particular, the invention enables the laser emission to be stabilizedin such manner that the power emitted by one of its beams corresponds tothe central dip in the power curve of this beam, stabilization beingachieved by a control means in which variations in length of theresonant cavity are corrected with reference to the difference in phasedetected between the variation of the length of this cavity and thecorresponding modulation of the emitted laser signal. The principaladvantages of the method according to the invention resides in the factthat for a given optical length of the laser apparatus, the centralfrequency of the emission of a laser ray is perfectly defined, accountbeing taken of the existance of suitable pressure and excitationconditions permitting simultaneous emission of at least two adjacentlaser beams.

These suitable operating conditions are as follows:

a. A low pressure in the laser enclosure such that the collision widthis considerably less than the Doppler width. In these conditions thelaser operates on a nonhomogeneous beam, that is to say that the systemis operating on the basis of one group of molecules only, among all themolecules in a state of inversion and present in the distribution curvefor the molecular population as a function of the energies of themolecules. This curve, which is known as the N (:1) curve, is also knownas the gain distribution curve or as the molecular gain'distributioncurve.

b. Saturation of the gain, obtained by using strong energizationassociated with a minimum energy-output connection. The non-linearity ofthe amplifying medium limits the output power to a value which is lowerwhen passing through the central transition frequency than at itsimmediately contiguous frequency zones.

c. the presence of a stationary field: the laser wave is constituted bytwo progressive waves having opposite wave vectors, and is made up fromtwo groups of molecules of opposite axial velocities which each form adownward bend in the gain distribution curve, as a function of thevelocities.

The CO to which the method is applied, on the one hand fulfils the threeconditions set forth above, and on the other hand is sufficientlystopped down as to function on the fundamental TEM, system. Thedifferent beams can be emitted simultaneously and their power stems froma single distribution of the N(v) populations. If the length of thecavity of a laser of this kind is altered, the relative frequencypositions of the modes of the cavity and of the molecular gain vary. Asa result of depopulation in the molecular gain distribution created by aplurality of beams, there is obtained, in the case of certain cavitylengths, an effect, which is similar in principle to the Lamb dip, butwhich differs therefrom in that it is not necessarily central and inthat it is possible to fix its position as regards frequency.

The method of the present invention which makes it possible to adjustwith great precision the emission of a C laser to suit the wave-lengthrequired, consists, after the wave-lengths It, and 80 2 have beenselected, in predetermining by calculation the length L of the resonantcavity, as follows, for example:

in constructing the CO laser that fulfils the abovestated conditions andin adjusting the length of the resonant cavity so as to obtain a dip atthe center of the power curve for the beam at wave-length I These andother objects and advantages of the invention will become apparent fromthe following description of an embodiment with reference to theaccompanying drawings, which relate to a mode of performing the methodin the case of regulation of the length of the resonant cavity of a C0laser by observing the dips in the profiles of the P and P beams in thev v, transition.

It will be recalled that P J connotes the transition that takes placebetween the J4 and .I energy levels, the frequency of the emittedradiation being related to the I level in question by the known formula:

in which:

11 is the central frequency of the transition B= 7.7 Joule, and h thePlanck constant.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 illustrates laser apparatusequipped for regulation in accordance with the present invention.

FIG. 2 illustrates the variations in the power curves of the P and Pbeams of the v v, transition when the length of the resonant cavityvaries.

FIG. 3 illustrates, on a greater scale, the power curves of the P and Pbeams as a function of the length of the resonant cavity.

FIG. 4 shows the comparative curve for the phases of the modulated lasersignal and an alternating voltage modulating the length of the resonantcavity.

FIg. 5 illustrates schematically a laser apparatus with control circuitsin accordance with the invention.

FIG. 6 shows curves recorded upon starting up and during the operationof the laser apparatus controlled in accordance with the invention.

DESCRIPTION OF ILLUSTRATED EMBODIMENT The two ends of the tube I shownin FIG. I are con stituted by windows 2 made of rock salt, which form anangle known as the Brewster angle with the transverse plane of the tube;a stream of carbon dioxide gas (not shown) circulates under low pressurein this tube 1. The resonant cavity is formed by two mirrors disposedperpendicularly to the axis of the tube, one of these mirrors 3 beingfixed, whereas the other 4 can be slowly displaced perpendicularly toitself, as indicated by the arrow 5. Two spectrographs 6 and 7 are sopositioned that they receive part of the radiation emitted in thetube 1. One of these spectrographs selects the beam having a wave-lengthof A and the other selects the beam having a wave-length of A and therelative power of these beams is indicated by the cells 8 and 9 whichrespectively detect each of these radiations.

FIG. 2 illustrates an example of the power curves for the two beams A,and M, as detected for example by the cells, 8 and 9, these curves beingsimultaneously recorded on a two-channel recorder, while the length ofthe resonant cavity is increased.

In this Figure, the power curve for the beam P having a wave-length A isshown in solid lines and that for the beam P having a wave-length of Xis shown in broken lines. For a given length of the resonant cavity thepower curves for the two beams P and P are in a given position such asthat indicated by the encircled numeral 21, and it an be seen that inthis position the curve for the beam P has a dip at 10 which correspondsto the position of the maximum for the beam P As the length of thecavity increases (towards the right in the Figure), the dip in the curvecorresponding to the beam P moves towards the center thereof, and onreaching the position shown by encircled numeral 27 it is preciselycentered in the same way as the curve corresponding to the beam P As thelength of the resonant cavity continues to increase, the dip in thepower curve for the beam P moves to the right together with the maximumof the curve for the beam P as shown in the sequence of graphs denotedby encircled numerals 27 to 33 in FIG. 2.

FIG. 2 shows that, by the method of the invention, the length of theresonant cavity can be adjusted so that the power curves for the beams Pand P correspond to the case illustrated at 27 in this Figure. When thisadjustment is made, it is then certain that the radiation emitted fromthe cavity closely corresponds to the two wave-lengths:

X 10.53111. for the beam P A 10.590p. for the beam P The method of theinvention can be used whenever it is required to ascertain withprecision a wave-length emitted by a multi-frequency laser apparatus.

In certain applications of laser radiation, it is particularly importantto know precisely what the wave-length of the radiation is, particularlywhere the system is used in spectroscopy or in tele-communications. Itwill be observed that the radiation emitted by carbon dioxide gas lasersis within a range of wave-lengths in the vicinity of 10.6 microns. Onthe other hand, the length of the laser tube is generally in the orderof 1 meter, that is to say times the wave-length of the radiationemitted, so that the stability required over the wave-length isequivalent to a stability over the length of the tube that is l0greater. A further object of the invention is to provide means forcontrolling the length of the laser tube such that the power emitted byone of the laser beams correspond to the central dip in the curverepresenting the power of this beam as a function of the length of thetube.

In FIG. 3 there is shown, as a solid line, the power curve for the beamP for the A A, transition of the carbon dioxide gas laser, while thebroken line curve is that for the beam P for the same transition. Thiscurve is recorded with the help of apparatus constituted by a laser tubeand two selective filters associated with two radiation detectors eachtuned to the emission wavelength of one of the beams, while the resonantcavity of the laser tube is extended by displacement by one of themirrors. During the course of this extension, the frequencies of theradiation emitted by the two beams vary as they pass through theircentral values A, and )t At this moment, the power of the beam P is atits maximum, whereas on the other hand, the power of the beam P passesthrough a minimum at this said position The length of the resonantcavity is held under control at this minimum which corresponds to awelldefined length of said cavity.

The comparative phase curve shown in FIG. 4 for the modulated signalemanating from the radiation emitted by the laser on the one hand and ofthe A.C. voltage fed to the piezo-electric ceramic element (to bedescribed with reference to FIG. 5) on the other is positive when thetwo phases are of the same sign, and negative when the two phases are ofopposite signs, and the value of the ordinate of this curve varies inproportion to the phase difference. The phase difference is cancelledout at the two maxima and at the minimum of the power curve shown inFIG. 3. This correspondence between the power of the signal and thephase difference is utilized in the control apparatus illustrated inFIG. 5.

In FIG. 5, the laser tube 11, together with the two mirrors 12' and 13,constitutes the resonant cavity of the apparatus. The mirror 13 ismovable and can be displaced slowly axially while remaining parallel toitself as indicated by the arrow l4, whereas the mirror 12, which isalso movable, ismounted on a piezo-electric ceramic element 15, the end16 of which is fixed and the length of which varies as a function of thevoltage applied to its feed terminal 17. This feed terminal 17 isconnected, by means including a condenser 18, to an output terminal 19of an oscillator 20, the output frequency of which is 475 cycles persecond, for example. This AC. voltage imparts, through the intermediaryof the piezo-electrical ceramic element 15, a reciprocating movement tothe mirror 12 and consequently modulates the laser radiation emitted inthe resonant cavity at the same frequency, i.e. 475 c.p.s., again usingthe example selected.

The mirror 13, containing a hole at its center enables the laser beam 21to pass out of the cavity, this beam being divided into two parts by asemi-reflecting mirror 22. A first part of said beam passes through theoptical filter 23, on the outlet side of which the filtered radiationstrikes the sensitive surface of a detector cell 24,

the output terminal 25 of which, receiving a voltage which is a functionof the laser energy and is modulated at the same frequency as this, isconnected to the input terminal 26 of the amplifier 27, the outputterminal 28 of which is connected to the input terminal 29 of asynchronous detector 30. Said synchronous detector 30, through itssecond input terminal 3i, connected to the output terminal 32 of theoscillator 20, receives as a reference the modulation frequency, i.e.475 c.p.s. in the example selected. A voltage, the sign of which ispositive when the two input voltages are of the same phase, and negativewhen the same input voltages are of opposite phase, and the amplitude ofwhich is proportional to the adjustment that is to be made to the lengthof the resonant cavity, is received at the output terminal 33 of thissynchronous detector 30, which terminal is connected on the one hand tothe first input terminal 3 of a two-channel recorder 45, and on theother, to the input terminal 36 of an integrator 37. The integrator 37consists of an amplifier 38 shunted by a capacitance 39. The outputterminal 40 of the integrating circuit 37 is connected to the inputterminal 41 of an amplifier 42, the output terminal 43 of which isconnected to the feed terminal 17 of the piczo-elcctric ceramic unit 15.

For stating up and controlling the apparatus of the invention, use ismade of the second portion of the laser beam 21, i.e. the portion whichpasses through semireflecting mirror 22. Said second portion passesthrough the optical filter 44 and strikes the sensitive face of thedetector cell 45. The output terminal 46 of said detector cell isconnected to the input terminal 47 of an amplifier 48, the outputterminal 49 of which is connected to the second input terminal 50 of thetwochannel recorder 35.

The curve for the power emanating from the laser emitter is thusrecorded in this second channel of the recorder as a function of time,whereas the output voltage curve of the synchronous detector 30 isrecorded in the first channel of the same recorder. FIG. 6 shows, by wayof example, two curves as recorded on the recorder 35.

When the apparatus in accordance with the invention is started up, onlythe second terminal of the recorder is operative. When the mirror 13 isdisplaced in a uniform manner in the direction of the arrows 14, thecurve for the power of the laser emission, corie's' ibfidfiigidihe beamF of the l v-M transition, as a function of the length of the resonantcavity, is recorded in said second channel. In this way, there areobtained curves 51, 52 and 53 of FIG. 6, in which curves can be observedthe displacement of the dip A to the right and the centering of said dipon the curve 53 when the length of the cavity increases. As explainedabove, the emission frequency is then accurately known, and it is thenparticularly desirable to set the length of the resonant cavity at thisprecise moment.

The movement of the mirror 13, which has been used to effect coarseadjustment of the length of the cavity, is stopped; a sawtooth voltage,varying regularly between 1,500 and +1 ,500 volts for example, is thenapplied to the feed terminal of the piezo-electrical ceramic unit 15 byway of the synchronous detector 30, brought to the fine adjustmentposition. An automatic switching arrangement provides for movement fromthe fine adjustment position to the control position when the curve 54reaches its central minimum at B. This switching action on the one handstabilizes the sawtooth voltage at its momentary value and, on the otherhand, brings the oscillator and the controlloop system into operation.

Thereafter, two curves are registered in the two channels of therecorder: curve 55, representing slight variations in the power of thelaser emission stabilized in accordance with the invention is recordedin the second channel, and curve 56, representing variations in the DC.voltage applied to the feed terminal of the piezo-electrical ceramicunit is recorded in the first channel.

The method can be used with molecular gas and multi-frequency lasers, bylimiting the laser emission to two or three beams.

We claim:

1. A method for selectively stabilizing a multifrequency laser at one ormore preselected frequencies wherein said laser emits a plurality ofbeams each having a corresponding frequency, wavelength and power curve,the method comprising selecting at least two of said plurality of beams,adjusting the optical length of the resonant cavity of said laser to alength substantially equal to the value L where L is defined by theequation:

utilizing said point as a reference point, monitoring the output of saidlaser to detect any shift of said dip from said reference point, andfurther adjusting said optical length so that said dip is maintained atsaid point.

2. A method for selectively stabilizing a multifrequency laser at one ormore preselected frequencies wherein said laser emits a plurality ofbeams each having a corresponding frequency, wavelength and power curve,the method comprising selecting at least two of said plurality of beams,adjusting the optical length of the resonant cavity of the laser to alength approximately equal to the value L where L is defined by theequation:

k,, k k, are whole numbers 0;

A A A, are the preselected wavelengths;

n is the index of refraction of the resonant cavity; so that said powercurves of said selected beams appear at the same time, monitoring thepower curve of the most energetic of said selected beams, cyclicallymodulating the optical length of said resonant cavity, cyclicallymodulating the laser emission, detecting the phase difference betweenthese two modulations, deriving a signal from said phase difference,using said signal for further adjusting said optical length to anoperating point which corresponds to the minimum of a dip appearing inthe power curve of said most energetic beam, and regulating by means ofsaid optical length of said resonan cavity for stabilizing said laser asaid operating point, whereby said laser is stabilized at saidpreselected frequencies.

3. The method according to claim 2 wherein said further adjusting stepof the optical length of the cavity is made such as to obtain a centraldip in said power curve of said most energetic selected beam at a pointbetween peaks of equal amplitude and to maintain the operating point ofthe laser at said point.

1. A method for selectively stabilizing a multi-frequency laser at oneor more preselected frequencies wherein said laser emits a plurality ofbeams each having a corresponding frequency, wavelength and power curve,the method comprising selecting at least two of said plurality of beams,adjusting the optical length of the resonant cavity of said laser to alength substantially equal to the value L where L is defined by theequation:2nL k1 lambda 1 k2 lambda 2 . . . ki lambda i where k1, k2 . .. ki are whole numbers >0; lambda 1, lambda 2 . . . lambda i are thepreselected wavelengths; n is the index of refraction of the resonantcavity; so that a central dip occurs at a point between two peaks ofequal amplitude in the most energetic of said power curves associatedwith said selected beams, utilizing said point as a reference point,monitoring the output of said laser to detect any shift of said dip fromsaid reference point, and further adjusting said optical length so thatsaid dip is maintained at said point.
 2. A method for selectivelystabilizing a multifrequency laser at one or more preselectedfrequencies wherein said laser emits a plurality of beams each having acorresponding frequency, wavelength and power curve, the methodcomprising selecting at least two of said plurality of beams, adjustingthe optical length of the resonant cavity of the laser to a lengthapproximately equal to the value L where L is defined by theequation:2nL k1 lambda 1 k2 lambda 2 . . . kii where k1, k2 . . . ki arewhole numbers >0; lambda 1, lambda 2 . . . lambda i are the preselectedwavelengths; n is the index of refraction of the resonant cavity; sothat said power curves of said selected beams appear at the same time,monitoring the power curve of the most energetic of said selected beams,cyclically modulating the optical lEngth of said resonant cavity,cyclically modulating the laser emission, detecting the phase differencebetween these two modulations, deriving a signal from said phasedifference, using said signal for further adjusting said optical lengthto an operating point which corresponds to the minimum of a dipappearing in the power curve of said most energetic beam, and regulatingby means of said optical length of said resonant cavity for stabilizingsaid laser at said operating point, whereby said laser is stabilized atsaid preselected frequencies.
 3. The method according to claim 2 whereinsaid further adjusting step of the optical length of the cavity is madesuch as to obtain a central dip in said power curve of said mostenergetic selected beam at a point between peaks of equal amplitude andto maintain the operating point of the laser at said point.